# INTERSECTION THEORY

@inproceedings{Lauritzen2007INTERSECTIONT, title={INTERSECTION THEORY}, author={Niels Lauritzen and Johan P. Hansen}, year={2007} }

I provide more details to the intersection theoretic results in [1]. CONTENTS 1. Transversality and tubular neighborhoods 1 2. The Poincaré dual of a submanifold 4 3. Smooth cycles and their intersections 8 4. Applications 14 5. The Euler class of an oriented rank two real vector bundle 18 References 20 1. TRANSVERSALITY AND TUBULAR NEIGHBORHOODS We need to introduce a bit of microlocal terminology. We begin by reviewing a few facts of linear algebra. If V is a finite dimensional real vector… Expand

#### 2,073 Citations

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A conjecture on vanishing and non-negativity of intersection multiplicity on the blow-up of a regular local ring at its closed point has been proposed. Proofs of vanishing, several special cases of… Expand

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To each subset I of {1, . . . , k} associate an integer r(I). Denote by X the collection of those n × k matrices for which the rank of a union of columns corresponding to a subset I is r(I), for all… Expand

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The geometry of complex subspaces contained within real subspaces of a complex vector space is described in detail in Section 2. This leads to an analysis of real subbundles of a complex vector… Expand

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Let X = G/P be a homogeneous space and ek be the class of a simple coroot in H2(X). A theorem of Strickland shows that for almost all X, the variety of pointed lines of degree ek, denoted Zk(X), is… Expand

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Abstract Let A be a noetherian commutative ring of dimension d and L be a rank one projective A -module. For 1 ≤ r ≤ d , we define obstruction groups E r ( A , L ) . This extends the original… Expand

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This paper introduces a general method for relating characteristic classes to singu-larities of a bundle map. The method is based on the notion of geometric atomicity. This is a property of bundle… Expand

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Let SUX(r) be the moduli space of semi-stable vector bundles of rank r with trivial determinant over a connected smooth projective algebraic curve X of genus g ≥ 1 over C. Recall that a vector bundle… Expand

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